Vertex method for computing functions of fuzzy variables
TL;DR: The vertex method can avoid abnormality due to the discretization technique on the variables domain and the widening of the resulting function value set due to multi-occurrence of variables in the functional expression by conventional interval analysis methods.
About: This article is published in Fuzzy Sets and Systems.The article was published on 1987-09-21. It has received 550 citations till now. The article focuses on the topics: Feedback vertex set & Fuzzy number.
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TL;DR: The objective of this paper is to critically review the emerging non-probabilistic approaches for uncertainty treatment in finite element analysis and gives a state-of-the-art of the interval finite element algorithms available from literature.
352 citations
TL;DR: In this paper, a non-probabilistic fuzzy approach and a probabilistic Bayesian approach for model updating for non-destructive damage assessment is presented. But the model updating problem is an inverse problem prone to ill-posedness and ill-conditioning.
338 citations
TL;DR: The transformation method is introduced as a powerful approach for both the simulation and the analysis of systems with uncertain model parameters based on the concept of α-cuts, a special implementation of fuzzy arithmetic that avoids the well-known effect of overestimation.
327 citations
01 Jan 2000
TL;DR: This chapter is an overview of past and present works dealing with fuzzy intervals and their operations, and contains a reasoned survey of methods for comparing and ranking fuzzy intervals.
Abstract: This chapter is an overview of past and present works dealing with fuzzy intervals and their operations. A fuzzy interval is a fuzzy set in the real line whose level-cuts are intervals. Particular cases include usual real numbers and intervals. Usual operations on the real line canonically extend to operations between fuzzy quantities, thus extending the usual interval (or error) analysis to membership functions. What is obtained is a counterpart of random variable calculus, but where, contrary to the latter case, there is no compensation between variables. Many results pertaining to basic properties of fuzzy interval analysis are summed up in the chapter. Computational methods are presented, exact or approximate ones, based on parametric representations, or level-cut approximations. The generalized fuzzy variable calculus involving interactive variables is also discussed with emphasis on triangular-norm based fuzzy additions. Dual ‘optimistic’ operations on fuzzy intervals, i.e., with maximal error compensation are also presented; its interest lies in providing tools for solving fuzzy interval equations. This chapter also contains a reasoned survey of methods for comparing and ranking fuzzy intervals. The chapter includes some historical background, as well as pointers to applications in mathematics and engineering.
314 citations
TL;DR: Mixed, probabilistic/non-probabilistic uncertainty modeling is dealt with in the framework of imprecise probabilities possessing the selected components of evidence theory, interval probabilities, and fuzzy randomness by means of interval modeling and fuzzy methods.
252 citations
References
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TL;DR: Much of what constitutes the core of scientific knowledge may be regarded as a reservoir of concepts and techniques which can be drawn upon to construct mathematical models of various types of systems and thereby yield quantitative information concerning their behavior.
12,530 citations
01 Jan 1975
8,942 citations
TL;DR: A method to deal with multiple-alternative decision problems under uncertainty by considering each of these variables as fuzzy quantities, characterized by appropriate membership functions of fuzzy sets induced by mappings is proposed.
737 citations
TL;DR: A computational algorithm based on the α-cut representation of fuzzy sets and interval analysis is described which provides a discrete but exact solution to extended algebraic operations in a very efficient and simple manner.
540 citations
Book•
01 Dec 1983
TL;DR: A new approach to analyze the risks a computer system may be subject to and a non-numeric method that allows natural language expression is presented.
Abstract: A new approach to analyze the risks a computer system may be subject to. A non-numeric method that allows natural language expression is presented. A tutorial for implementation of the ideas of fuzzy set theory in general, and of the linguistic approach to risk analysis in particular, are discussed
362 citations